Because of the Trinity, One God in three Persons, we can appreciate that “God is love” (1 John 4:8). Our theology proper teaches us about God’s nature, so as His image-bearers we reflect God as we love Him and one another.
Because of the Gospel, that Christ died for us while we were still sinners, we can appreciate that such a sacrifice is how “God shows His love for us” (Romans 5:8). The center of history, the death of Jesus on the cross, demonstrates God’s love, so He calls us to love one another just as He loved us (John 13:34).
Because of our Lord’s command to remember His death in the ordinance of communion (Luke 22:19), and because our weekly liturgy as a church includes the sharing of the Lord’s Supper, we regularly eat and drink in remembrance of Christ’s love.
Doctrine/truth drives our doing/obedience. We love the truth about God’s love and the truth about His love continually works on us and in us and out of us into love for one another.
So individualistic communion is ironic at best and impious at worst. Though our salvation is personal, it’s not mostly about “me and Jesus” but about “Jesus and us.”
Eat and drink the signs of love. Put on the clothes of love, it binds everything together in perfect harmony (Colossians 3:14). Love does no wrong to a neighbor; therefore love is the fulfilling of the law.